Chemical Equilibrium

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Chemical Equilibrium

• Chapter 13
• Zumdahl

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Chemical Equilibrium

• If a chemical system that can react is isolated,
  it will eventually reach EQUILIBRIUM.
• No loss or gain of reactants or products
• Concentrations of all reactants and products
  remain constant with time.

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Chemical Equilibrium

• Chemical equilibrium is a DYNAMIC state.
• individual molecules continue to collide and
  react
• rate of forward reaction rate of reverse
  reaction

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The Law of Mass Action

• For the balanced reaction
• jA kB lC mD
• The equilibrium expression is
• K CeqlDeqmAeq-jBeq-k

products reactants
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Law of Mass Action

• The exponents in the equilibrium constant are the
  stoichiometric coefficients of the balanced
  reaction
• The equilibrium constant defined this way is not
  uniquely determined for a particular reaction

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Equilibrium Expression

• 4NH3(g) 7O2(g) 4NO2(g) 6H2O(g)

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Equilibrium Expression

• Multiplication by a constant
• 8NH3(g) 14O2(g) 8NO2(g) 12H2O(g)

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Equilibrium Expression

• Reverse Reaction
• 4NO2(g) 6H2O(g) 4NH3(g) 7O2(g)

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Notes on Equilibrium Expressions (EE)

• When the equation for a reaction is multiplied by
  n, Knew (Koriginal)n
• The Equilibrium Expression for a reaction is the
  reciprocal of that for the reaction written in
  reverse.
• The units for K depend on the explicit
  representation of the reaction being considered.

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Reactions involving gases Kp

• jA kB lC mD
• if A, B, C, and D are all gases, partial
  pressure can be used instead of concentration

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Reactions that involve gases

• Concentration of a gas can be expressed in two
  ways
• Volume occupied c (n/V)
• Pressure P (n/V) RT
• The two ways are related P c RT
• So are the corresponding equilibrium expressions
• Kp Kc(RT)(Dn)

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Relating K to Kp for a gas reaction

• For
• jA kB lC mD
• Kp K(RT)Dn
• Dn sum of coefficients of gaseous products
  minus
• sum of coefficients of gaseous reactants.

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Heterogeneous Reactions

• How can we define the concentration of a solid or
  a liquid in a meaningful way ?
• The concentration of pure liquids and solids is
  assumed to be unity (and unitless) when gaseous
  reactants/products are involved

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Heterogeneous Equilibria

• CaCO3(s) CaO(s) CO2(g)
• K CO2
• The position of a heterogeneous equilibrium does
  not depend on the amounts of pure solids or
  liquids present.

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Reaction Quotient

• . . . helps to determine the direction of the
  move toward equilibrium.
• The law of mass action is applied with initial
  concentrations.

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Reaction Quotient (continued)

• H2(g) F2(g) 2HF(g)

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The Law of Mass Action

• For the balanced reaction
• jA kB lC mD
• The equilibrium expression is
• K CeqlDeqmAeq-jBeq-k

products reactants
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Q and K for a reaction
K is defined only for equilibrium concentrations
products _at_ equilibrium reactants _at_ equilibrium
Q may defined for any set of concentrations
Q gt K too many products rxn will go Q lt K
not enough products rxn goes
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Solving Equilibrium Problems

• 1. Balance the equation.
• 2. Write the equilibrium expression.
• 3. List the initial concentrations.
• 4. Calculate Q and determine the shift to
  equilibrium.

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Solving Equilibrium Problems(continued)

• 5. Define equilibrium concentrations.
• 6. Substitute equilibrium concentrations into
  equilibrium expression and solve.
• 7. Check calculated concentrations by calculating
  K.

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Sample Problem
At equilibrium, NH3(g), N2(g) and H2(g) have the
following concentrations NH3 3.1 10-2
M N2 8.5 10-1 M H2 3.1 10-3 M What
is K for the reactions N2(g) 3H2(g) 2NH3(g)
N2(g) H2(g) NH3(g) 2NH3(g) N2(g) 3H2(g)
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Sample Problem
(a) N2(g) 3H2(g) 2NH3(g)
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Sample Problem
From initial NH3(g), N2(g) and H2(g)
concentrations of H2 1.00 M N2 2.00
M NH3 3.00 M In which direction will the
equilibrium N2(g) 3H2(g) 2NH3(g)
(K6.02x10-2 M-2) proceed?
Q 32 x 2-1 x 1-3 M-2 13.5 Q gtgt K means
reaction will proceed to left
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Solving Equilibrium Problems

• Write the balanced chemical reaction
• Write the appropriate expression for the
  equilibrium constant
• List the initial concentrations (calculate Q) I
• Define the change (unknown) necessary to reach
  equilibrium C
• Apply this change to get the equilibrium (E)
  concentrations in terms of this unknown quantity

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Solving Equilibrium Problems(continued)

• Substitute into the expression for K (or Kp) and
  solve for the unknown quantity
• Choose the most appropriate solution
• Check resulting equilibrium constant for
  self-consistency

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ICE Table
Find the equilibrium position of a reaction
mixture that is initially PNO2 1.0 atm. Kp
0.25 atm-1. 2 NO2 (g) N2O4 (g)
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ICE table for 2NO2 N2O4
Kp PN2O4/P2NO2 gt 0.5x/(1.0-x)2 0.25 x
0.268
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Solving Quadratic Equation

• ax2 bx c 0
• x (-b (b2 - 4ac)1/2)/2a
• OR
• x (-b - (b2 - 4ac)1/2)/2a

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Approximate Solutions

• Small x approximation
• Applicable either when the reaction mixture
  starts out close to equilibrium
• Equilibrium constant (Kc) is small
• Assume x is negligible
• compared to other numbers in the problem
• Use to simplify the algebra

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Example

• Kp for the equilibrium
• N2 (g) 3 H2 (g) ltgt 2 NH3 (g)
• is 4.51 x 10-5 at 450 o C.
• Initially 5.00 atm N2 and 5.00 atm H2 are sealed
  in a vessel. What is the equilibrium partial
  pressure of NH3 ?

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ICE Table for N23H2 2NH3
Kp P2NH3 / (P3H2 PN2)
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• (2x)2 / (5.0-3x)3 (5.00-x) 4.51x10-5
• 4x2 / 5.03 5.00 4.51x10-5 (small x approx)
• x 0.0839
• Check for validity !!!
• P (NH3) 2 x atm 0.168 atm

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Exercises Heterogeneous Equilibria
What is the equilibrium expression for (a)
PCl5(s) PCl3(l) Cl2(g) (b) CuSO4 5H2O(s)
CuSO4(s) 5H2O(s)
(a) KP PCl2 (b) KP PH2O5
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Le Châteliers Principle

• . . . if a change is imposed on a system at
  equilibrium, the position of the equilibrium will
  shift in a direction that tends to reduce that
  change.

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Using Le Chateliers Principle

• Think of stress in terms of changes in
  concentration
• Think of the effect of such changes in terms of
  the law of mass action
• Reaction Quotient may be a useful concept

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Predicting direction of change

• Calculate Q using given concentrations
• Compare Q with K
• If Q lt K reaction proceeds to the RIGHT
• If Q gt K reaction proceeds to the LEFT
• If Q K system is at equilibrium

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How do you take a reaction to completion ?

• Add lots of one type of reagent ?
• Remove products as they are formed ?
• Add a catalyst ?
• Change the temperature ?
• Change the pressure ?

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Example

• N2 (g) 3 H2 (g) ltgt 2 NH3 (g)
• K NH32eq / N2eqH23eq
• Q NH32 / N2H23
• Taking a reaction to completion means setting up
  the conditions so that Q ltlt K

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Temperature --- A Reagent ?

• Consider heat or enthalpy as a reactant or
  product necessary for reaction.
• A 2B C D DH0 -70 kJ/mol
• Exothermic means products have less heat than
  reactants, so heat is a product
• Endothermic means products have more heat than
  reactants, so heat is a reagent
• Increasing the temperature gt add heat

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Effect of Pressure

• How can we change pressure ?
• Change volume gt concentration changes
• Add gas (reagent) gt concentration changes
• Add gas (buffer) gt concentration ???

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• Suppose Q K when we start
• Reduce volume by factor of 2.0
• New concentrations are ALL doubled
• Q (2 NH3eq)2 / (2N2eq)(2H2eq)3
• K (22 )/ (2)(2)3
• 0.25 K

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Effect of Increasing Pressure

• Increasing pressure by reducing volume favors
  side with less amounts of gas
• 2H2O (g) ltgt 2H2 (g) O2 (g)

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Effect of Catalyst

• kf Af exp (- Ea,f /RT)
• kr Af exp (- Ea,r /RT)
• Catalysts reduce effective barrier
• kfcat Af exp (- (Ea,f - DE)/RT) kf e - DE/RT
• krcat Af exp (- (Ea,r - DE) /RT) kr e -DE/RT
• At equilibrium kf conc.. kr conc..

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Effect of Catalyst

• No change in equilibrium position !!!
• Catalysts change the rate of a reaction without
  being consumed
• Catalysts change mechanism
• Equilibrium is governed by the overall reaction
  (and stoichiometry)

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Effects of Changes on the System

• 1. Concentration The system will shift away
  from the added component.
• 2. Temperature K will change depending upon the
  temperature (treat the energy change as a
  reactant).

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Effects of Changes on the System (continued)

• 3. Pressure
• a. Addition of inert gas does not affect the
  equilibrium position.
• b. Decreasing the volume shifts the
  equilibrium toward the side with fewer moles.

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Group Discussion

• There is only one value of the equilibrium
  constant for a particular system at a particular
  temperature, but an infinite number of
  equilibrium positions

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Summary (Chapter 13)

• Equilibrium is dynamic
• Law of mass action
• equilibrium depends only on the overall reaction,
  not on the mechanism (i.e., determined by
  stoichiometry)
• Equilibrium constant vs. Reaction Quotient
• Le Chateliers principle